arXiv:2604. 13082v2 Announce Type: replace-cross Abstract: Grokking in transformers trained on algorithmic tasks is characterized by a long delay between training-set fit and abrupt generalization, but the source of that delay remains poorly understood.
The paper presents quantitative generalization bounds for fixed‑precision transformer models, addressing both in‑distribution statistical generalization and length generalization. It derives guarantees based on model parameters, quantization space, and alphabet size, and shows how training length and sample size trade off, with longer training being exponentially more efficient. Experiments confirm the theoretical predictions.
arXiv:2512. 01870v3 Announce Type: replace Abstract: We study whether a transformer network can learn the deterministic sequence of trees generated by the iterated prime factorization of the natural numbers.
arXiv:2609.08851v1 Announce Type: new Abstract: Recent advancements in transformer length generalization theory enable us to reliably predict when a transformer can learn to solve a task. In particul...
arXiv:2603. 17019v2 Announce Type: replace Abstract: A central question in the debate over large language models is whether transformers can learn rules they have never seen, or whether they can only interpolate: predict new cases from their similarity to training examples.
arXiv:2608.31067v1 Announce Type: new Abstract: Learning generalizable algorithmic computations remains a challenge for neural networks, as reflected in persistent failures on compositional and lengt...
The Recurrent Looped Transformer (RLT) divides its layers into a parallel causal encoder and a recurrent decoder, allowing the computation path to grow with sequence length while keeping a fixed per-token cost. Experiments on six algorithmic tasks show that RLT outperforms a standard eight‑layer Transformer, achieving perfect generalization on parity up to 256 bits and high accuracy on swap‑based permutation tracking and modular arithmetic beyond training lengths. Ablation studies confirm that the recurrent feedback is essential for these gains, with chunked updates preserving performance on parity but reducing accuracy on permutation tracking.
Scaling Large Language Models (LLMs) has been driven mainly by enlarging the Transformer backbone, but for an already-strong model this requires another round of costly pretraining. We study whether an existing backbone can keep improving by allocating more computation to each token while leaving the Transformer backbone fixed.
arXiv:2610.07676v1 Announce Type: cross Abstract: Research on transformer expressivity shows whether a transformer is capable of solving a given task, but gives little indication of whether the solut...
arXiv:2610.32104v1 Announce Type: cross Abstract: Several formal theories have been developed to characterize the capabilities and limitations of the transformer architecture, each employing differen...
arXiv:2605. 22488v2 Announce Type: replace Abstract: Structured prompts require integrating components according to task-relevant relations.
arXiv:2604. 25800v2 Announce Type: replace Abstract: Chain-of-Thought (CoT) has been shown to empirically improve Transformers' performance, and theoretically increase their expressivity to Turing completeness.